Waverider or wave follower buoys are used to measure the amplitude and frequency of waves. These buoys contain in their interior an accelerometer, a cassette recorder, batteries and the electronics. Once the buoy is anchored in its position, the cassette unit records the wave amplitude signals given by the accelerometer at intervals of one (1) second for about twenty (20) minutes each four (4) hours. The lenghts and intervals of the recording can be varied.
To insure the correctness of the signals given by the accelerometer it is imperitive to calibrate it periodically. For this purpose, it is necessary to induce on the buoy a sinusoidal or simple harmonic motion, and adjust the accelerometer within the buoy until the amplitude signals given by this accelerometer produce the sinusoidal motion. In order to insure that the accelerometer is functioning appropriately for variable amplitudes and frequencies of the sinusoidal motion, it is necessary to calibrate it for several amplitudes and frequencies of such motion, for example, for amplitudes of one (1) to four (4) meters and periods of three (3) to forty (40) seconds.
There are four known methods for testing the calibration of waver rider buoy accelerometers.
1. RUBBER MOORING SHOCK CORD METHOD: This method consists simply in hanging the buoy 32 from a crane using a rubber mooring shock cord 30 (Diameter=3.6 cm, stiffness=60 newtons/m) as is shown in FIG. 1. Using a rope 34 the buoy 32 is pulled down until it barely touches the ground; then the rope 34 is released thus the buoy 32 will start moving. A pointer 31 fixed on the buoy 32 shows the motion on a scale 33. The rubber cord 30 has a spring like characteristic with damping, therefore the waverider buoy 32 will exhibit a damped sinusoidal motion.
This method of calibration is fairly simple and inexpensive; however, there are several disadvantages which are explained as follows:
(A) Due to the rubber cord's 30 own damping characteristics, the motion induced to the waverider buoy 32 is also damped (damped sinusoidal).
(B) The amplitudes that can be induced to the waverider buoy 32 are limited to the length of the rubber cord 30. If the rubber cord 30 is stretched more than its linear elastic limit (tear=500 newtons/cm.sup.2), then the motion induced on the Waverider buoy 32 is nonsinusoidal.
(C) In order to increase the frequency of motion induced to the Waverider buoy 32, it is necessary to shorten the length of the rubber cord 30, thus introducing the problem mentioned in (b) above.
(D) Some sort of a crane or tall fixture is needed in order to hook the upper end of the rubber mooring cord 30. The length of the rubber mooring cord 30 used in this method ranges from ten (10) to fifteen (15) meters.
The rubber mooring cord method is not very accurate, due to the damped motion induced on the buoy 32, since for calibration purposes a periodic simple harmonic or sinusoidal motion is needed.
2. SPRINGS METHOD: In this method the Waverider buoy is connected to a counter-balance weight 36 by a non-stretchable steel wire rope 38 as shown in FIG. 2. This steel wire rope 38 is forced to pass on two pulleys 30 (or a large diameter wheel) fixed to the ceiling. The bottom of the Waverider buoy 42 and of the counterbalance weight 36 is connected to the ground by means of springs 44 with the same spring constant. The counterbalance weight 36 has a poiner 46 which indicates on a scale 48 the amplitude of the motion. The starting motion is given to the system manually. The frequency of the damped sinusoidal motion induced to the buoy 42 can easily be changed by adding springs or using springs of different spring constant.
Eventhough this method is fairly simple and is an improvement relative to the Rubber Mooring Shock Cord method, it also presents some disadvantages. These are:
(a) Due to the springs 44 own damping characteristics, the motion induced to the Waverider buoy 42 is also damped (damped sinusoidal).
(b) The amplitude of the motion that can be induced to the waverider buoy 42 is very limited in relation to the size of the rig due to the limitation in the springs 44 lengths. If large amplitudes are desired, then the springs 44 will over-stretch thus surpassing their linear elastic limit, therefore the motion induced to the buoy 42 would be nonsinusoidal and unacceptable.
3. PENDULUM METHOD: This method is basically a combination of horizontal swinging of a pendulum 50 and a purely vertical oscillation on a vertical test stand, as is shown in FIG. 3. There, a steel wire cord 54 connects the buoy 52 with a counterbalance weight 56 around a drum 58 attached to the pendulum bar. The counterbalance weight 56 has a pointer attached to it 60 which shows the amplitude on a scale 62. The amplitude of the sinusoidal motion induced to the Waverider buoy 52 is controlled by the amplitude of motion imparted to the swinging pendulum 50. The frequency of oscillation can be increased or decreased by shortening or lengthening the distance between the pendulum weights and the oscillation pivot, or by simply reducing or increasing the weight of the pendulum. The method is fairly accurate provided the weight used for the pendulum is heavy enough, however, there are also the following disadvantages:
(a) The motion produced by a swinging pendulum 50 exhibits aproximate sinusoidal motion only for small oscillation amplitudes of the pendulum 50. Therefore, the amplitudes induced to the Waverider buoy 52 are also small.
(b) In order to change the frequency of oscillation either the weight 50 of the pendulum, or its length, or both must be varied. If the weight 50 of the pendulum is too light, then the motion induced to the Waverider buoy 52 is not sinusoidal, and if its length is too short then the amplitude of motion induced to the buoy is too small as was pointed out in (a) above.
(c) If larger amplitudes of sinusoidal motion are desired, then it would be necessary to build an unrealistically large apparatus, thus cost, physical space and other problems would arise.
(d) The vertical oscillations induced to the Waverider buoy 52 are in reality damped sinusoidal since the pendulum's amplitude is reduced at each stroke; thus it is necessary for a person to continually give the pendulum 50 a push in order to maintain an approximately constant pendulum amplitude.
This method can also be combined with the springs method by connecting with springs the Waverider buoy 52 and the counterbalance weights 56 to the ground.
4. VERTICAL ROTATING ARM METHOD: This method consists in placing the buoy 64 on a vertical rotating arm 68. The arm rotates about a fixed point, therefore the buoy 64 describes a circular path. Since the accelerometer inside the buoy 64 only reacts to vertical displacements, the motion that the accelerometer actually sees is a sinusoidal or simple harmonic.
FIG. 4 shows the test apparatus. There the rotating arm 68 may be set in motion by an electric motor or variable angular velocity. The high RPM of the electric motor is reduced to 2 to 25 RPM by a system of timing belts which connect the motor to the rotating arm 68. The Waverider buoy 64 is kept in its upright position by a combination of gears and chains. There is a counterbalance weight 66 at the arm end opposite to where the Waverider buoy 64 is fixed. The amplitude of the sinusoidal motion induced to the buoy 64 can be either 1, 2 or 3 meters. This method is accurate, since the amplitude of motion can be exactly measured, and the frequency can be precisely controlled, however, this method also presents the following disadvantages:
(a) There is no known test apparatus built for testing 6900 series Waverider buoys. The only one built are for testing strictly 6000 series waverider buoys which are of smaller size and weight. (b) Changing the amplitude takes about one day as it is necessary to reposition the buoy mounting and also reposition the counterbalance weights 66.
(c) The amplitude settings are limited to either 1, 2 or 3 meters.
(d) There is a limitation on the maximum angular velocity that can be induced to the Waverider buoy 64 since it is required for the horizontal acceleration to stay well below 0.5 g.
(e) The actual physical space taken up by the apparatus is large. For larger amplitudes, an even larger apparatus would be required.
(f) Needs to be well anchored since an improper balance between Waverider buoy 64 and the counterbalance weight 66 could cause serious problems at larger angular velocities.